Question

The ratio of P-wave to S-wave velocities, Vp/Vs, within the Earth depends on

• A. bulk modulus
• B. shear modulus
• C. density
• D. coefficient of internal friction

Hint:

For the ratio \(V_p/V_s\), both the bulk modulus (which influences P-waves) and the shear modulus (which influences S-waves) are important factors. Keep in mind that both of these moduli contribute to the velocities of seismic waves.

Answer 1

The Correct Option is A, B

Step 1: Understanding P-wave and S-wave Velocities
The P-wave (primary wave) and S-wave (secondary wave) are seismic waves that travel through the Earth. P-waves are compressional waves, and S-waves are shear waves. The velocities of these waves depend on the properties of the Earth's materials.

Step 2: Relationship Between P-wave and S-wave Velocities
The velocity of P-waves (V_p) and S-waves (V_s) is influenced by the material's bulk modulus, shear modulus, and density. However, the ratio of P-wave to S-wave velocities (V_p/V_s) primarily depends on both the bulk modulus and shear modulus of the material.

Step 3: Comparing the Options
Bulk modulus: This affects the velocity of P-waves. Since P-waves are compressional, the bulk modulus plays a significant role in determining their velocity.
Shear modulus: This affects the velocity of S-waves, which are shear waves. The shear modulus directly influences S-wave velocity and therefore impacts the V_p/V_s ratio.
Density: Affects both P-wave and S-wave velocities but does not influence the ratio as strongly as the moduli.
Coefficient of internal friction: This is not a key factor in determining the ratio of P-wave to S-wave velocities.